def dc_calc_kloosterman(modulus, number):
arg = request.args.get("val", [])
if not arg:
return flask.abort(404)
try:
a, b = map(int, arg.split(','))
if modulus == 1:
# there is a bug in sage for modulus = 1
return r"""
\( \displaystyle K(%s,%s,\chi_{1}(1,·))
= \sum_{r \in \mathbb{Z}/\mathbb{Z}}
\chi_{1}(1,r) 1^{%s r + %s r^{-1}}
= 1 \)
""" % (a, b, a, b)
from dirichlet_conrey import DirichletGroup_conrey
chi = DirichletGroup_conrey(modulus)[number]
chi = chi.sage_character()
k = chi.kloosterman_sum_numerical(100, a, b)
real = round(k.real(), 5)
imag = round(k.imag(), 5)
if imag == 0:
k = str(real)
elif real == 0:
k = str(imag) + "i"
else:
k = latex(k)
return r"""
\( \displaystyle K(%s,%s,\chi_{%s}(%s,·))
= \sum_{r \in \mathbb{Z}/%s\mathbb{Z}}
\chi_{%s}(%s,r) e\left(\frac{%s r + %s r^{-1}}{%s}\right)
= %s. \)""" % (a, b, modulus, number, modulus, modulus, number, a, b, modulus, k)
except Exception, e:
return "<span style='color:red;'>ERROR: %s</span>" % e
def dc_calc_kloosterman(modulus, number):
arg = request.args.get("val", [])
if not arg:
return flask.abort(404)
try:
a, b = map(int, arg.split(','))
if modulus == 1:
# there is a bug in sage for modulus = 1
return r"""
\( \displaystyle K(%s,%s,\chi_{1}(1,·))
= \sum_{r \in \mathbb{Z}/\mathbb{Z}}
\chi_{1}(1,r) 1^{%s r + %s r^{-1}}
= 1 \)
""" % (a, b, a, b)
from dirichlet_conrey import DirichletGroup_conrey
chi = DirichletGroup_conrey(modulus)[number]
chi = chi.sage_character()
k = chi.kloosterman_sum_numerical(100, a, b)
real = round(k.real(), 5)
imag = round(k.imag(), 5)
if imag == 0:
k = str(real)
elif real == 0:
k = str(imag) + "i"
else:
k = latex(k)
return r"""
\( \displaystyle K(%s,%s,\chi_{%s}(%s,·))
= \sum_{r \in \mathbb{Z}/%s\mathbb{Z}}
\chi_{%s}(%s,r) e\left(\frac{%s r + %s r^{-1}}{%s}\right)
= %s. \)""" % (a, b, modulus, number, modulus, modulus, number, a, b,
modulus, k)
except Exception, e:
return "<span style='color:red;'>ERROR: %s</span>" % e
